U.S. patent number 9,154,440 [Application Number 13/848,430] was granted by the patent office on 2015-10-06 for system and method for identifying multiple paths between network nodes.
This patent grant is currently assigned to Google Inc.. The grantee listed for this patent is Google Inc.. Invention is credited to Zhengrong Ji, Yuguang Wu, Junlan Zhou.
United States Patent |
9,154,440 |
Zhou , et al. |
October 6, 2015 |
System and method for identifying multiple paths between network
nodes
Abstract
Aspects of the invention pertain to transmitting packet data
across a computer network. The packets may be sent via one or more
distinct routes from a source to a destination. Each route may
employ multiple routers disposed along the network. Non-colliding
routes are determined by transmitting pairs of probe packets along
the routes. A first probe packet has a maximal length, and a second
probe packet has a minimal length. Depending on the order of
arrival of the probe packets, the system determines whether two
transport layer ports at the destination device collide. If there
is a collision, then the system searches for a set of non-colliding
ports. Once the non-colliding ports are determined, application
data may be sent as packets along the different routes to those
ports.
Inventors: |
Zhou; Junlan (Sunnyvale,
CA), Ji; Zhengrong (Sunnyvale, CA), Wu; Yuguang
(Santa Clara, CA) |
Applicant: |
Name |
City |
State |
Country |
Type |
Google Inc. |
Mountain View |
CA |
US |
|
|
Assignee: |
Google Inc. (Mountain View,
CA)
|
Family
ID: |
43526932 |
Appl.
No.: |
13/848,430 |
Filed: |
March 21, 2013 |
Prior Publication Data
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Document
Identifier |
Publication Date |
|
US 20130215766 A1 |
Aug 22, 2013 |
|
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
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12533187 |
Jul 31, 2009 |
8432801 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H04L
45/00 (20130101); H04L 45/24 (20130101); H04L
47/622 (20130101); H04L 45/128 (20130101); H04L
43/12 (20130101) |
Current International
Class: |
H04L
12/863 (20130101); H04L 12/701 (20130101); H04L
12/26 (20060101); H04L 12/707 (20130101) |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
International Search Report and Written Opinion PCT/US2010/043662,
Date of Mailing Apr. 26, 2011. cited by applicant .
Canadian Office Action for Application No. 2,769,722 dated Nov. 5,
2013. cited by applicant.
|
Primary Examiner: Lam; Yee
Attorney, Agent or Firm: Gordon; Edward A. Lanza; John D.
Foley & Lardner LLP
Parent Case Text
CROSS-REFERENCE TO RELATED APPLICATIONS
The present application is a continuation of U.S. patent
application Ser. No. 12/533,187, filed Jul. 31, 2009, the
disclosure of which is incorporated herein by reference.
Claims
The invention claimed is:
1. A method for identifying ports to support data packet traffic
between a source device and a destination device in a computer
network, the method comprising: selecting a subset S.sub.k.sup.D
from a set S.sub.D of destination ports p the destination device is
configured to listen to, the subset S.sub.k.sup.D for serving the
data packet traffic between the source device and the destination
device; choosing a port in the set S.sub.D for analysis that is not
a member of the subset S.sub.k.sup.D; determining whether the
chosen port collides with any of the ports in the subset
S.sub.k.sup.D by analyzing one or more pairs of packets transmitted
to the destination device and evaluating whether the packets from
at least one of the pairs arrive out of order; wherein, when there
is a collision involving the chosen port, eliminating the chosen
port from the set S.sub.D; and when it is determined that there is
no collision, modifying the subset S.sub.K.sup.D according to the
following equation: S.sub.K.sup.D.sub.modified=S.sub.K.sup.D U
{chosen port }, wherein U indicates a union operation.
2. The method of claim 1, further comprising repeating the
selecting, choosing, determining and eliminating operations for one
or more rounds, wherein a new port is chosen in each of the one or
more rounds.
3. The method of claim 2, wherein after each port that does not
collide with any of the ports in the subset S.sub.D.sup.K is
identified, the method further comprises sending the data packet
traffic from the source device to the destination device via at
least two of the non-colliding ports.
4. The method of claim 1, wherein for a given one of the one or
more pairs of packets, a first packet of the given pair is of a
maximum packet transmission size.
5. The method of claim 4, wherein a second packet of the given pair
of packets is of a minimum packet transmission size.
6. The method of claim 1, wherein the chosen port is randomly
selected from the set S.sub.D.
7. The method of claim 1, wherein the destination device sends an
acknowledgement to the source device upon the arrival of the one or
more pairs of packets.
8. A processing system for transmission of data packets between a
source device and a destination device in a computer network, the
computer network including a plurality of nodes for routing the
data packets between the source and destination devices, the
processing system comprising: a memory for storing data; and a
processor operatively coupled to the memory for reading the data
from and writing the data to the memory, the processor being
configured to select a subset S.sub.k.sup.D from a set S.sub.D of
ports p the destination device is configured to listen to, the
subset S.sub.k.sup.D being configured to serve the data packets
between the source device and the destination device, the processor
being further configured to choose a port in the set S.sub.D for
analysis that is not a member of the subset S.sub.k.sup.D, to
determine whether the chosen port collides with any of the ports in
the subset S.sub.k.sup.D by analyzing one or more pairs of packets
transmitted to the destination device and evaluating whether the
packets from at least one of the pairs arrive out of order,
wherein, when there is a collision involving the chosen port, the
processor eliminates the chosen port from the set S.sub.D; and when
it is determined that there is no collision, the processor modifies
the subset S.sub.k.sup.D according to the following equation:
S.sub.K.sup.D.sub.modified=S.sub.k.sup.D U {chosen port}, wherein U
indicates a union operation.
9. The processing system of claim 8, wherein the processor
comprises the source device.
10. The processing system of claim 8, wherein the processor is
further configured to repeating the selecting, choosing,
determining and eliminating operations for one or more rounds,
wherein a new port is chosen in each of the one or more rounds.
11. The processing system of claim 10, wherein after each port that
does not collide with any of the ports in the subset S.sub.D.sup.K
is identified, the system is configured to send the data packets
from the source device to the destination device via at least two
of the non-colliding ports.
12. The processing system of claim 8, wherein for a given one of
the one or more pairs of packets, a first packet of the given pair
is of a maximum packet transmission size.
13. The processing system of claim 12, wherein a second packet of
the given pair of packets is of a minimum packet transmission
size.
14. The processing system of claim 8, wherein the chosen port is
randomly selected from the set S.sub.D.
15. The processing system of claim 8, wherein the source device is
configured to receive an acknowledgement from the destination
device upon the arrival of the one or more pairs of packets.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates generally to routing data in computer
networks. More particularly, the invention pertains to identifying
multiple paths between source and destination nodes in computer
networks.
2. Description of Related Art
With a networked computer, it is possible to increase the
communication bandwidth or the availability of network connectivity
by using multiple interfaces concurrently to aggregate bandwidth.
One strategy of bandwidth aggregation is known as Link Aggregation
("LAG"). Another is known as Equal Cost Multiple Path ("ECMP").
Such strategies allow router or switch nodes in the network to load
balance traffic across multiple outgoing links. The outgoing link
of a packet is often determined based on the hash value of
information (source IP address, destination IP address, source
port, destination port) in the packet header. A node may maximize
its application throughput to a destination by identifying a set of
port pairs (source port, destination port) to send traffic across
multiple paths available to the destination.
However, specific implementations of such bandwidth allocation,
e.g., the use of hashing functions on switches/routers, are often
proprietary. Furthermore, the results of such hashing functions may
depend on the seed value of individual switches. It is not feasible
for a source node to determine a priori if port pairs are to be
hashed to different paths to a destination node, especially in wide
area network where end hosts have little knowledge of network
topologies and router/switch configurations in between them.
In contrast, the invention provides non-proprietary systems and
methods that identify and employ multiple paths between network
nodes.
SUMMARY OF THE INVENTION
In one embodiment, a method for identifying ports to support data
packet traffic between a source device and a destination device in
a computer network is provided. The method comprises setting a set
S.sub.D of destination ports p the destination device is configured
to listen to; selecting a subset S.sub.k.sup.D from the set S.sub.D
for serving the data packet traffic between the source device and
the destination device; choosing a port p in the set S.sub.D for
analysis; determining whether the chosen port p collides with any
of the ports in the subset S.sub.k.sup.D; and if there is a
collision involving the chosen port p, eliminating the chosen port
p from the set S.sub.D.
In one example, the chosen port p is removed from the set S.sub.D
prior to determining whether there is a collision. In another
example, if there is no collision, the method further comprises
modifying the subset S.sub.K.sup.D according to the following
equation: S.sub.K.sup.D.sub.modified=S.sub.K.sup.D U {p}. In this
case, the method may further comprise repeating the selecting,
choosing, determining and eliminating operations for k rounds,
wherein a new port p is chosen in each round. In one alternative,
after each port p is identified that does not collide with any of
the ports in the subset S.sub.D.sup.K, the method further comprises
sending the data packet traffic from the source device to the
destination device via at least two of the non-colliding ports.
In another example, determining whether the chosen port p collides
with any of the ports in the subset S.sub.k.sup.D includes
transmitting a pair of probe packets from the source device to the
destination device. In one alternative, a first one of the pair of
probe packets is of a maximum packet transmission size. In this
case, a second one of the pair of probe packets may be of a minimum
packet transmission size. And in a further example, the port p is
randomly selected from the set S.sub.D.
In accordance with another embodiment, a method of determining port
collisions when transmitting traffic between a source device and a
destination device in a computer network is provided. The method
comprises setting a set S.sub.D of destination ports p the
destination device is configured to listen to; selecting a subset
S.sub.k.sup.D from a set S.sub.D for serving the data packet
traffic between the source device and the destination device;
initializing a test subset of ports S.sub.Y to be equal to
S.sub.K.sup.D; choosing a port p' from the set S.sub.Y and choosing
a port p from the set S.sub.D but not in S.sub.k.sup.D for
analysis; sending a pair of probe packets from the source device to
the destination device via p and p'; evaluating arrivals of the
pair of the probe packets at the destination device to determine if
there is a collision at ports p and p'; and if there is no
collision, then identifying port p as a selected port for
transmitting data packets between the source device and the
destination device.
In one example, the destination device sends an acknowledgement to
the source device upon the arrival of the pair of probe packets.
Here, the acknowledgement may identify whether there is a collision
between p and p'.
In another example, the port p' is removed from S.sub.Y upon
choosing. In this case, the method may further comprise repeating
the choosing, sending, evaluating and identifying operations for
each port in S.sub.Y until all of the ports have been removed from
S.sub.Y.
In yet another example, a first one of the pair of probe packets is
of a maximum packet transmission size and a second one of the pair
of probe packets is of a minimum packet transmission size. In this
case, a collision may be determined if the pair of probe packets
are received in order of transmission.
In accordance with another embodiment, a processing system for
transmission of data packets between a source device and a
destination device in a computer network is provided. Here, the
computer network includes a plurality of nodes for routing the data
packets between the source and destination devices. The processing
system comprises a memory for storing data and a processor
operatively coupled to the memory for reading the data from and
writing the data to the memory. The processor is configured to
select a subset S.sub.k.sup.D from a set S.sub.D of ports p the
destination device is configured to listen to. The subset
S.sub.k.sup.D is configured to serve the data packet traffic
between the source device and the destination device. The processor
is further configured to choose a port p in the set S.sub.D for
analysis, to determine whether the chosen port p collides with any
of the ports in the subset S.sub.k.sup.D, and, if there is a
collision involving the chosen port p, to eliminate the chosen port
p from the set S.sub.D.
In one example, the processor determines whether the chosen port p
collides with any of the ports in the subset S.sub.k.sup.D by
transmitting a pair of probe packets to the destination device. In
this case, the processor may determine whether there is a collision
based upon an order of arrival of the transmitted probe packets. In
an alternative, the processor comprises the source device.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 illustrates a computer network for use with aspects of the
invention.
FIG. 2 illustrates aspects of a network having multiple routes in
accordance with the invention.
FIG. 3 is a flow diagram for identifying suitable paths to a given
destination port according to aspects of the invention.
FIG. 4 is a flow diagram for determining collisions among ports of
a destination node according to aspects of the invention.
FIG. 5 illustrates cross traffic increasing dispersion in a
network.
And FIG. 6 illustrates cross traffic decreasing dispersion in a
network.
DETAILED DESCRIPTION
Aspects, features and advantages of the invention will be
appreciated when considered with reference to the following
description of preferred embodiments and accompanying figures. The
same reference numbers in different drawings may identify the same
or similar elements. Furthermore, the following description is not
limiting; the scope of the invention is defined by the appended
claims and equivalents.
FIG. 1 presents a schematic diagram of a computer network 100
depicting various computing devices that can be used in a networked
configuration in accordance with aspects of the invention. For
example, computer network 100 may have a plurality of computers
102, 104, 106 and 108 as well as other types of devices such as
portable electronic devices such as a mobile phone 110 and a PDA
112. Such computing devices may be interconnected via a local or
direct connection 114 and/or may be coupled via a communications
network 116 such as a LAN, WAN, the Internet, etc. The
communications network 116 may include multiple nodes comprising
switches or routers, as will be discussed below.
Each computing device may include, for example, one or more
processing devices (e.g., a CPU) and have user inputs such as a
keyboard 118 and mouse 120 and/or various other types of input
devices such as pen-inputs, joysticks, buttons, touch screens,
etc., as well as a display 122, which could include, for instance,
a CRT, LCD, plasma screen monitor, TV, projector, etc. Each
computer 102, 104, 106 and 108 may be a personal computer, server,
etc. By way of example only, computers 102 and 106 may be personal
computers while computer 104 may be a server and computer 108 may
be a laptop.
Each computer such as computers 102 and 104 contains a processor,
memory/storage and other components typically present in a
computer. For instance, memory/storage stores information
accessible by processor, including instructions that may be
executed by the processor and data that may be retrieved,
manipulated or stored by the processor. The memory/storage may be
of any type or any device capable of storing information accessible
by the processor, such as a hard-drive, ROM, RAM, CD-ROM, flash
memories, write-capable or read-only memories. The processor may
comprise any number processing elements, such as sub-processing
units operating in a parallel-processing configuration.
Alternatively, the processor may be a dedicated controller for
executing operations, such as an ASIC.
The communications network 116 is preferably configured to handle
data packets (e.g., packets P.sub.1 and P.sub.2) using one or more
nodes. FIG. 2 illustrates a network configuration 200, where a
source device 202 (e.g., computer 102) may send data to a
destination device 204 (e.g., computer 104) via one or more nodes
206 in the network. As shown, each node may comprise a
router/switch such as router R.sub.0, R.sub.I, etc.
The routers may include a processor such as a CPU, as well as
memory for storing/queuing buffered data packets. The packets are
preferably queued in a first-in, first-out ("FIFO") order. The
routers may be arranged in the network so that packets from the
source device 202 may be passed to the destination device 204 via
multiple alternative routes. Identifying such routes enables the
system to efficiently route the packets. By way of example, FIG. 2
illustrates a first path 208 along the route R.sub.0, R.sub.L,
R.sub.L+1.sup.1, R.sub.M.sup.1 and R.sub.M+1, as well as a second
path 210 along the route R.sub.0, R.sub.L, R.sub.L+1.sup.2,
R.sub.M.sup.2 and R.sub.M+1.
In accordance with aspects of the invention, several propositions
or requirements regarding analyzing packet routing through the
network are set forth. The first proposition is that there is no
out of order delivery of packets sent from the source device to the
destination device if these packets traverse the same route, unless
a link failure occurs and causes a route change at a router in
between its transmissions of these packets.
A second proposition is that if two consecutive packets traverse
different routes, they may arrive out of order at the destination.
The probability of out of order delivery is maximized when the size
of first probe packet is maximized and that of second probe packet
is minimized.
And a third proposition is that if two consecutive probe packets
P.sub.1 and P.sub.2 of respective lengths L.sub.max and L.sub.min
(e.g., the largest and smallest packet lengths supported by node
R.sub.0) traverse different routes yet arrive in order at the
destination, the path traversed by P.sub.2 experiences much larger
queuing and/or transmission delay than P.sub.1. In this case, it
may be of little gain to split the data traffic across the two
paths traversed by P.sub.1 and P.sub.2, since the throughput
improvement is marginal.
Assume source device 202 is configured to initiate a data intensive
application (such as a file transfer) that sends a large amount of
traffic (e.g., 10 Mbytes) from its port X to destination device
204. According to one aspect, S.sub.D is defined as a set of
destination ports p the destination device 204 is listening to and
can receive data from the source device 202. In this embodiment,
the invention allows the source device 202 or other associated
device to discover N paths each served by a destination port in
S.sub.N.sup.D (S.sub.N.sup.D.OR right.S.sub.D) of the destination
device 204. The source device 202 thus can split its traffic across
these N paths, for example by establishing N TCP/UDP sessions, one
to each destination port in S.sub.N.sup.D.
In one embodiment, a process is executed iteratively to arrive at a
solution. FIG. 3 illustrates a flow diagram 300 for identifying
multiple paths to a given destination device and a set of ports on
the destination serving these paths. The process desirably executes
iteratively for up to N-1 rounds. As shown in block 302, a counter
k of the rounds is incremented (and which may be initialized to 0).
In the k.sup.th round, the process starts with S.sub.k.sup.D, which
is a subset of k ports in S.sub.D to serve traffic from the source
device to the destination device over k unique paths. This is done
to discover the (k+1).sup.th path from the source to the
destination, as well as a port p in S.sub.D to serve packets
traversing this path. This process is desirably done by exchanging
at least one probe pair or acknowledgement ("ACK") packet between
the source device and the destination device.
In one example, two destination ports, namely p.sub.1, and p.sub.2,
"collide" if packets destined to p.sub.1 traverse the same path as
those destined to p.sub.2. The source device (e.g., router R.sub.0
or source 202) searches for a port p in S.sub.D that does not
collide with any ports in S.sub.k.sup.D, and eliminates ports from
S.sub.D that collide with ports in S.sub.k.sup.D. First, in block
304 a port p is removed from S.sub.D. Preferably, the port p is
randomly selected for removal in block 304. Then, in block 306, it
is determined if the port p just removed from S.sub.D collides with
any port in S.sub.k.sup.D. If so, the removed port p is not added
back to S.sub.D such that it is skipped in the next round k+1, and
the process returns to block 302. If there is no collision, the
process proceeds to block 308, where S.sub.k+1.sup.D is assigned to
be S.sub.k+1.sup.D=S.sub.k.sup.D.orgate.p. Here, port p is added to
S.sub.k+1.sup.D. The ".orgate." symbol in this equation is a union
or addition operator.
As shown in block 310, if the counter k is less than N-1, then the
process returns to block 302; otherwise it ends at block 312.
To determine if a given port p collides with any port in
S.sub.k.sup.D without modifying S.sub.k.sup.D, the process 400
shown in FIG. 4 may be employed. First, as shown in block 401, a
set of ports S.sub.Y is initialized to be the same as the set of
ports in S.sub.K.sup.D. As shown in block 402, a port p' is removed
from the set S.sub.Y. The port p' is preferably randomly selected
for removal from S.sub.Y.
Next, as shown in block 404, for each port p' in S.sub.k.sup.D, a
pair of probe packets is sent back to back via ports p' and p
respectively. The size of the first probe packet is preferably a
maximum transmission unit (L.sub.MAX) supportable by the network
between the source 202 and the destination 204, while the second
probe is preferably of a minimum packet length (L.sub.MIN)
supported by the network between the source 202 and destination
204. The destination device 204 may send an acknowledgement ACK
back to the source device 202, as shown in block 406.
As shown in block 408, the ACK may indicate whether the ports p and
p' collide. In particular, if the destination device 204 received
the two probe packets out of order, it is determined that ports p'
and p do not collide at block 410. If the packets are received in
order, it is determined that p' and p collide (e.g., port p
collides with port p' in S.sub.K.sup.D) as shown in block 412.
As shown in block 414 if S.sub.Y is not empty, the process
preferably returns to block 402 and repeats until a port p' is
found in S.sub.Y that collides with p, or until it is determined
that no ports in S.sub.Y collides with p. If S.sub.Y is empty or a
collision is found, the process terminates at bock 416.
One of the propositions discussed above was that if two consecutive
packets traverse different routes, they could arrive out of order
at the destination. The probability of out of order delivery is
maximized when the size of first probe is maximized and that of
second probe is minimized.
To prove this observation, consider the following network model
depicting two routes between a source node and a destination node.
In this example, two probe packets, P.sub.1 of length L.sub.1, and
P.sub.2 of length L.sub.2, are sent back to back from the source
node to the destination node. The probe packets each traverses one
of two routes, which may initially share certain routers, e.g.,
R.sub.0, R.sub.1, . . . R.sub.1. In this example, the two routes
branch off after R.sub.1 and re-merge at R.sub.m. The transmission
rate of a router R
(R.epsilon.{R.sub.i|0.ltoreq.i.ltoreq.l}.orgate.{R.sub.i.sup.1|l<i.lto-
req.m}.orgate.{R.sub.i.sup.2|l<i.ltoreq.m}) is r(R), and
Q.sup.2(R) and Q.sup.1(R) represent the queuing delays experienced
by P.sub.1 and P.sub.2 at R, respectively.
Assume there is no cross traffic and the queuing delay is zero for
P.sub.1 and P.sub.2 at R.sub.0 to R.sub.1. It is straightforward to
prove that:
.times..function..ltoreq..ltoreq. ##EQU00001##
T.sub.l.sup.2 and T.sub.l.sup.2 are the arrival times of P.sub.1
and P.sub.2 at R.sub.1, and min{r(R.sub.i)|0.ltoreq.i.ltoreq.l} is
the bandwidth of bottleneck link between R.sub.0 and R.sub.1. When
there is cross traffic, T.sub.l.sup.2-T.sub.l.sup.1, the dispersion
of P.sub.1 and P.sub.er can expand or compress. To express this
phenomena, we let:
.times..function..ltoreq..ltoreq..delta. ##EQU00002##
Cross traffic, such as a packet P.sub.3 may be serviced in between
P.sub.1 and P.sub.2. As shown in FIG. 5, if this occurs, then the
dispersion between P.sub.1 and P.sub.2 increases. The probability
of such cross traffic expanding the dispersion of P.sub.1 and
P.sub.2 decreases with the length L.sub.2 of packet P.sub.2. Thus,
if the length L.sub.2 of packet P.sub.2 is minimized, the
probability of cross traffic packet P.sub.3 increasing the
dispersion between P.sub.1 and P.sub.2 is minimized.
If cross traffic P.sub.3 is serviced before P.sub.1 as shown in
FIG. 6, the dispersion of P.sub.1 and P.sub.2 is decreased. The
probability of such cross-traffic P.sub.3 decreasing the dispersion
of P.sub.1 and P.sub.2 increases with the length L.sub.1 of packet
P.sub.1. Furthermore, it can be proved that:
.gtoreq..times..function..ltoreq..ltoreq. ##EQU00003## .times.
##EQU00003.2##
.times..function..ltoreq..ltoreq..ltoreq..ltoreq..times..function..ltoreq-
..ltoreq. ##EQU00003.3##
Thus T.sub.l.sup.2-T.sub.l.sup.1 is minimized if L.sub.2 is
minimized and L.sub.1 is maximized. Next, T.sub.m.sup.1 and
T.sub.m.sup.2, the arrival times of P.sub.1 and P.sub.2 at R.sub.m,
respectively, and the condition for T.sub.m.sup.1>T.sub.m.sup.2,
that is P.sub.2 arrives at R.sub.m and eventually at the
destination node before P.sub.1 are derived. In particular:
.function..function..ltoreq..ltoreq..times..function..function.
##EQU00004##
.function..function..ltoreq..ltoreq..times..function..function.
##EQU00004.2##
T.sub.m.sup.2<T.sub.m.sup.1 if and only iff:
<.function..function..function..ltoreq..ltoreq..times..function..ltore-
q..ltoreq..times..function..ltoreq..ltoreq..times..function..ltoreq..ltore-
q..times..function. ##EQU00005##
In the above formula, when L.sub.1 is maximized and L.sub.2 is
minimized, T.sub.l.sup.2-T.sub.l.sup.1 is minimized, and
.function..ltoreq..ltoreq..times..function..ltoreq..ltoreq..times..functi-
on. ##EQU00006## is maximized. Assume the sum of queuing delays
experienced by P.sub.1 and P.sub.2,
.function..ltoreq..ltoreq..times..function..times..times..function..ltore-
q..ltoreq..times..function. ##EQU00007## are independent of L.sub.1
and L.sub.2. The probably of T.sub.m.sup.2<T.sub.m.sup.1 is
maximized when L.sub.1 is maximized and L.sub.2 is minimized.
It can be further proved that if between R.sub.m and the
destination node, P.sub.1 and P.sub.2 traverse on different routes,
the lead time of P.sub.2 over P.sub.1 is also maximized when is
L.sub.1 maximized and L.sub.2 is minimized.
With regard to the third proposition, if two consecutive probe
packets P.sub.1 and P.sub.2 of length L.sub.max and L.sub.min
(denoting the largest and smallest packet length supported by the
network's nodes) traverse different routes yet arrive in order at
the destination, the path traversed by P.sub.2 experience much
larger queuing and/or transmission delay than P.sub.1. It is thus
of little gain to split the application traffic across the two
paths traversed by P.sub.1 and P.sub.2, since the throughput
improvement is marginal.
When L.sub.1=L.sub.max and L.sub.2=L.sub.min, the probability of
cross traffic in between P.sub.1 and P.sub.2 is close to zero, and
it may be assumed that:
.times..function..ltoreq..ltoreq..ltoreq..ltoreq..times..function..ltoreq-
..ltoreq. ##EQU00008##
.ltoreq..ltoreq..times..function..ltoreq..ltoreq..times..function..functi-
on..function..ltoreq..ltoreq..times..function..ltoreq..ltoreq..times..func-
tion..function.> ##EQU00008.2##
.times..function..ltoreq..ltoreq..ltoreq..ltoreq..times..function..ltoreq-
..ltoreq..times..function..function..function..ltoreq..ltoreq..times..func-
tion..ltoreq..ltoreq..times..function..function.>
##EQU00008.3##
If the queuing delays of P.sub.1 and P.sub.2 are equal,
.times..function..ltoreq..ltoreq..ltoreq..ltoreq..times..function..functi-
on..ltoreq..ltoreq..times..function..function.> ##EQU00009##
Once a pair of non-colliding ports has been found, the system may
configure packet transmission to send one or more packets along the
different routes from the source node to the destination node. In
one alternative, the system evaluates the network to determine
whether more than two non-colliding destination ports are present.
If so, the packet traffic may be split among all non-colliding
routes.
Furthermore, the processes discussed herein, such as the operations
discussed with regard to FIGS. 3 and 4, may be performed by one or
more processors in the system. By way of example only, processing
may be performed by the source device 202, destination device 204
or one of the routers 206 of FIG. 2. The processor(s) may execute a
program recorded/stored on a computer-readable recording medium,
such as ROM, RAM, flash memory, CD-ROM, DVD-ROM or the like.
Although aspects of the invention herein have been described with
reference to particular embodiments, it is to be understood that
these embodiments are merely illustrative of the principles and
applications of the present invention. It is therefore to be
understood that numerous modifications may be made to the
illustrative embodiments and that other arrangements may be devised
without departing from the spirit and scope of the invention as
defined by the appended claims.
* * * * *